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Caristi Fixed Point Theorem in Metric Spaces with a Graph

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  • M. R. Alfuraidan
  • M. A. Khamsi

Abstract

We discuss Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with graph.

Suggested Citation

  • M. R. Alfuraidan & M. A. Khamsi, 2014. "Caristi Fixed Point Theorem in Metric Spaces with a Graph," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, March.
    • Handle: RePEc:hin:jnlaaa:303484
    DOI: 10.1155/2014/303484
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    Cited by:

    1. Karim Chaira & Abderrahim Eladraoui & Mustapha Kabil & Samih Lazaiz, 2018. "Extension of Kirk-Saliga Fixed Point Theorem in a Metric Space with a Reflexive Digraph," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-6, February.
    2. P. Charoensawan & W. Atiponrat, 2017. "Common Fixed Point and Coupled Coincidence Point Theorems for Geraghty’s Type Contraction Mapping with Two Metrics Endowed with a Directed Graph," Journal of Mathematics, Hindawi, vol. 2017, pages 1-9, November.
    3. Shamoona Jabeen & Zhiming Zheng & Mutti-Ur Rehman & Wei Wei & Jehad Alzabut, 2021. "Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations," Mathematics, MDPI, vol. 9(5), pages 1-14, March.

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